The Cost of Dichotomization

“…amount to maintain the statistical power reached before dichotomization, that is, by an amount of =2 ¼ 1:57 if only one variable is dichotomized, and by an amount of 2=4 ¼ 2:44 if both variables are dichotomized, which represents the cost of dichotomization, as already calculated in Cohen (1983).”

“For example, dichotomizing a predictor at its median reduces variance explained in a normally distributed outcome by 38%, with further reductions as the dichotomization point moves away from the median [34].”

“This was a small effect by Cohen’s (1988) standards (d=.”

“As a result, it can obscure nuanced differences between categories and may lead to a loss of information [28–32].”

“…binary pornography consumption categories (no consumption vs. any consumption) reduce measurement precision and between-person variance and therefore lead to smaller correlations than a measure more sensitive to differential amounts of pornography consumption (Cohen, 1983; Hunter & Schmidt, 1990).”

“Additionally, continuous measures provide increased statistical power to detect effects, relative to dichotomous comparisons (Cohen, 1983; MacCal-lum et al., 2002).”

“That is, transforming continuous data into categorical, discrete, or binary data may result in a loss of information of individual differences and statistical power (Cohen, 1983; MacCallum et al., 2002).”

“Furthermore, the transformation of data will cause a reduction in statistical power, which requires a significant increase in the sample size to offset the issue (Cohen, 1983).”

“We acknowledge the drawbacks of dichotomizing variables and provide further correlation analysis to reinforce the findings of the mixed-model ANCOVA, with SHCV as a continuous predictor (Cohen, 1983; Royston et al., 2006).”

“…such a continuous (more accurately, graduated) response format is better able to capture differences in cooperation and defection than a dichotomous choice format (see Clark & Watson, 1995; Cohen, 1983, for detailed discussions on the (dis)advantages of dichotomous vs. continuous choice formats).”

“We conducted this analysis well aware of the fact that dichotomizing variables leads to information loss and reduces the statistical power to detect effects (Cohen, 1983).”

“There is little gained by such a procedure [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17].”

“However, estimates of odds ratios may be less valid than other effect size types (e.g., Cohen, 1983; Durlak, 2009; Hsu, 2004; Hunter & Schmidt, 2004) and are very sensitive to base rates (Ruscio, 2008).”

“The dichotomization of outcomes may result in a reduction of effect sizes (Cohen 1983).”

“However, several authors have argued against categorization of continuous variables (see, e.g., Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002; McClelland, Lynch, Irwin, Spiller, & Fitzsimons, 2015) as it lowers the information concerning individual differences and therefore affects the…”

“We also chose not to have categorical or dichotomous outcome variables as there is a risk of losing one to two thirds of the information on the variance of the total sample [65].”

“, “infected”/“non-infected”), a substantial number of false (-positive and -negative) results will occur (24).”

“The use of continuous scores also helps to overcome bimodality (Hicks, 1985; Wiggins, 1992) and improves statistical power (Cohen, 1983).”

“First, with one exception, the measures that had been used to assess SVO yielded only low-resolution output (e.g. categorical data), which restricts variance and thereby also the statistical power to detect effects (e.g. Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“…model slightly understates the reliability of the latent continuous true score, an expected result given that the dichotomization significantly inflates s 2 e (Cohen, 1983), particularly when the number of items is low (see also Supplemental Appendix D in the online version of the journal).”

“As such, we recommend researchers consider collecting continuous stance measures for tuning purposes, particularly since continuous measures are known to contain more statistical information than binary variables which can aid model performance (Altman and Royston 2006; Cohen 1983).”

“Second, it reduces the statistical power of hypothesis tests, making it harder to detect genuine effects (e.g., Cohen 1983).”

“Given admonitions from methodologists to avoid dichotomized variables (e.g., Cohen, 1983; Hunter & Schmidt, 1990), the tendency for editors and reviewers to reflexively dismiss results produced by binary assessments of pornography use is understandable.”

“We expected this modification to help normalize donation rates to preserve statistical power and analyze donations as a continuous measure (Cohen, 1983).”

“The AD-related preventive behaviors variable exhibited relatively low reliability, most likely as it was based on dichotomous responses [63] and covered different domains (e.”

“Since the variable is symmetrically distributed, it is dichotomised at the mean (Cohen 1983): coded as low if neither partner gave a score higher than 7.”

“Moreover, the dichotomization of continuous variables, that has to occur in factorial designs, has also been associated with a loss of statistical power (e.g., Baayen, 2004; Cohen, 1983).”

“is arguably unethical since it discards information, effectively decreasing the sample size (32) and, in turn, the ability to quantify (or rule out) meaningful intervention effects.”

“Denn das Bündeln der Daten zu Gruppen geht mit einem Informationsverlust einher, der sich auf die Validität auswirkt (Cohen 1983).”

“Attitude and involvement were dichotomised to transform them to categorical variables and correlate scores with mean (Cohen 1983).”

“Many researchers believe that otherthan Zoroastrianism, very few religions have put such anemphasis on purifying the soul and body, [24].”

“…with other groups using between-group comparisons, but shortcomings like the loss of information regarding individual differences, the loss of power and effect size, and the loss of measurement reliability remain (Cohen, 1983;MacCallum, Zhang, Preacher,&Rucker, 2002;Maxwell & Delaney, 1993).”

“…竞争性和个体性三种动机取向, 并且相同情境当中, 不同的动机取向可能会导致不同的行为(Deutsch, 1960)。随后, Messick和McClintock于 1968年采用 社会价值取向的概念, 并通过实验证实了人们对自 我-他人收益所赋予的权重存在个体差异(Messick & McClintock, 1968)。社会价值取向是个体对事件 重要性和价值的判断, 是一种相对稳定的人格倾向, 它与个体以往社会交往经验存在直接联系(Li, Zhu, Gummerum, & Sun, 2012)。 社会价值取向为描述决策者如何评价相互…”

“As we know, the statistical power is greatest when the sample is split at the medians of X and Y , and is always smaller than the power for the test on the equivalent continuous population r (Cohen, 1983; MacCallum et al., 2002).”

“Third, the simulation-based approach maintains heterogeneity within the subgroup because it estimates a weighted average of all the conditional effect estimates within the defined subgroup as opposed to categorization techniques which result in homogenous subgroups (Cohen, 1983).”

“Because of the well-described issues on dichotomizing continuous exposures in health science research 96,97 , we also estimated incident rate ratios of ;andre-calculatedtheregression-basedand g-estimationmediation-interactiondecompositionmodelssettingthe…”

“This also implies the analysis uses all the available information and is better statistically powered (Cohen 1983; Dawson and Weiss 2012; Norman 2010).”

“4.3.5 | Perceived stress scale Participants were asked to rate the extent to which they experienced negative emotions they identified as stress over the past month with the four‐item Perceived Stress Scale (PSS‐4; Cohen, 1983).”

“Second, the loss of power by dichotomizing variables at the median is equal to discarding one-third of the data (Cohen, 1983; MacCallum et al., 2002).”

“based on a discretized exposure typically have less power than tests based on the original, undiscretized exposure because discretizing throws away possibly relevant information (see, e.g. Cox, 1957; Cohen, 1983; Fedorov et al., 2009). Finally, causal estimates based on a discretized exposure have a more complicated i…”

“Categorisation has been shown to significantly decrease statistical power, resulting reduced sensitivity of an analysis to detect correlation [22, 23].”

“Central to these studies, is the degree to which assessment instruments execute their main objectives, validity, and predictive accuracy (Auerhahn, 1999, 2006; Blackmore & Welsh, 1983; Chaiken, Chaiken, & Peterson, 1982; Cohen, 1983; Greenwood & Abrahamse, 1982; Von Hirsch & Gottfredson, 1984).”

“The hierarchical approach is appropriate when the focus is on theory-based decisions to investigate the change in variations as a result of entering independent variables in the analysis over and above that contributed by independent variables entered initially in the analysis (Cohen, 1983).”

“In some occasions, the dichotomization of continuous data may result “in an increase of r over that of the original graduated variable; but these will be characterized by extreme skewness, heteroscedasticity, curvilinearity, e.g., step functions” (Cohen, 1983, p. 252).”

“It has been shown that categorizing measurement data also leads to attenuation of the Pearson correlation coefficient (see J. Cohen 1983; Bedrick 1995, and references therein).”

“To begin with, subgrouping should be reserved for categorical variables as otherwise it requires dichotomizing continuous moderators, usually using a median split, which reduces statistical power (Cohen, 1983; Steel & Kammeyer-Mueller, 2002).”

“The conversion process also reduces statistical power, necessitating a significant increase in sample size to compensate for the reduction (Cohen, 1983).”

“Transitioning to a continuous measurement of participants’ high-status motives allows us to better detect such potential differences (Cohen, 1983; DeCoster et al., 2009; MacCallum et al., 2002).”

“Third, research shows that dichotomizing continuous variables is statistically ill-advised and leads to an attenuation of power, loss of information, and biased estimates (Cohen, 1983; Dawson & Weiss, 2012; MacCallum et al., 2002; Royston et al., 2006).”

“Continuous phenotypes are known to provide more power for association studies than categorical phenotypes [13].”

“, forcible rape, forcible fondling, forcible sodomy, and sexual assault w/an object), age range, and relationship types, we conducted multiple Pearson chi-square analyses and evaluated the associated Cramer’s V effect sizes (Cohen, 1983).”

“…2013; Kim, Chen, Zhang, Simons-Morton, & Albert, 2013; MacCallum, Zhang, Preacher, & Rucker, 2002); yet its use has attracted criticism from some researchers who point to the potential to have misleading results due to proneness to both Type 1 and 2 errors (Cohen, 1983; Fitzsimons, 2008).”

“For instance, reducing a latent dimension into a dichotomous measure will artificially reduce the variance in the measure, markedly reducing statistical power (Cohen, 1983; MacCallum et al., 2002) and attenuating relationships between measures (Ruscio & Ruscio, 2002).”

“The problem with this approach is that it has been shown that the practice results in underestimates of effect sizes, reducing the sensitivity or power of statistical hypothesis tests ( Cohen, 1983 ).”

“…to a quantitative measure of frequency of use, entails a very discernible loss of information that in turn can result in a significant loss of statistical power (Altman and Royston, 2006; Cohen, 1983; Cox, 1957; Fedorov et al., 2009; MacCallum et al., 2002; Royston et al., 2006; Streiner, 2002).”